Question

If the line $2x+y+k=0$ is a normal to the parabola $y^2+8x=0$ then $k=$ ?

• A. $-16$
• B. $-8$
• C. $-24$
• D. $24$

Answer 1

The correct option is D $24$

For a line to be normal to a parabola we must have $c=-2am-a{m}^3$

where $m=$slope of line, $C=y$ intercept of line and $a$ is related to parabola

Given $2x+y+k=0$ is normal to the parabola $y^2+8x=0$

$so,y=-2x-kand{y}^2=-8kwhere,m=-2anda=-2so,-k=-2am-a{m}^3\Rightarrow -k=-2(-2)(-2)-(-2){(-2)}^3\Rightarrow k=24$